1. Field of the Invention
Entirely new quantum computers based on the quantum mechanics have been proposed with the expectation that they achieve a breakthrough in performance compared with the conventional computers based on the classical mechanics. The present invention relates to a basic logic gate for quantum computers, and particularly to a basic logic gate using a semiconductor quantum structure.
2. Description of the Related Art
In contrast to present computers based on the classical mechanics, quantum computers based on the principle of the quantum mechanics are proposed, and researches have been continued theoretically, that is, in respect to the software of the quantum computation so to speak. As for the hardware, however, conditions for implementing quantum logic gates physically are very severe, and hence the realization of them is still under development.
First, the principle of the quantum computation will be described. The conventional classical digital computer uses bits consisting of “0” and “1” as a basic computation element. In contrast, the quantum computer utilizes quantum bits consisting of two quantum states |0> and |1> that can assume superposition state.
For example, a particular quantum bit |a> is represented as follows.|a>=cos θ|0>+sin θ·exp(iα)|1>  (1)where α is a phase between |0> and |1>, and θ represents probability distribution of the states |0> and |1>. In other words, observing |a> will involve detecting |0> and |1> at ratios of cos2 θ and sin2 θ, respectively.
In 1995, Deutsh et. al. showed that combinations of two types of gates, “phase shifters” and “controlled Nots”, enable every logic operation of the quantum bits. Here, the phase shifter shifts the ratio (θ) of |0> and |1> and the phase α by a given amount as illustrated in FIG. 1. The controlled Not is a quantum gate concerning two quantum bits as illustrated in FIG. 2A, in which a first quantum bit is a control bit |a>, and a second quantum bit is a target quantum bit |b>. FIG. 2B is the truth table of its input/output signals. As for the operation of the controlled Not, although the target quantum bit |b> does not vary when the control quantum bit |a> is |0>, it works as a not gate that switches the target quantum bit |b> from |0> to |1> or vice versa when the control quantum bit |a> is |1>.
Since the quantum computation carries out the computation utilizing a “superposition state” in which the phase relationships between the quantum states have the quantum mechanical correlation, it must hold the “superposition state” during the computation. In an actual physical system, however, the superposition state is corrupted by decoherence factor (relaxation phenomenon) that disturbs the phase relationships (coherence). The relaxation phenomenon includes the phase relaxation (lateral relaxation) that disturbs the momentum of the system, and the energy relaxation (longitudinal relaxation) that disturbs the energy of the system. Among the two types of the relaxation, the phase relaxation occurs first, followed by the energy relaxation. In the system where the energy relaxation occurs very rapidly, the phase relaxation period becomes nearly equal to the energy relaxation period. The decoherence factor in a solid is mainly governed by the phase relaxation. Consequently, it is necessary to select a system with sufficiently long phase relaxation time, and to carry out the quantum computation in a much shorter time period than the phase relaxation time.
For this reason, to implement the quantum logic gates, the following conditions must be met: First, a system which has a long decoherence time, the time the coherence term takes to decay by a factor of e (the base of the natural logarithms), must be selected, and in which system the decoherence time (phase relaxation time) is much longer than the quantum operation time (basic gate time×the number of computations); and second, the elements essential for the quantum operation, that is, a one-quantum logic gate “phase shifter” and a two-quantum logic gate “controlled Not” must be constructed.
Not a few proposals of the quantum logic gates utilizing various types of physical systems have been made, and some of them report experimental examples with one to several quantum bits in early stages. Some representative examples are quantum computations utilizing 1) NMR, 2) ion trap, 3) linear optical system, and 4) semiconductor solid-state device.
As for 1) and 2), they are characterized in utilizing an atomic or molecular system with a very long decoherence time, and experimental examples with one to several quantum bits are reported. However, it is considered that the number of the bits of the operation is limited to a few quantum bits in the quantum computation utilizing the NMR, and to several quantum bits in the quantum computation utilizing the ion trap. Accordingly, they are unsuitable for large-scale computations that make full use of the characteristics of the quantum computation. In addition, since the quantum computation utilizing a linear optical system increases its scale with the number of the quantum bits, its computation performance is also limited to several quantum bits.
Thus, the quantum computation utilizing the semiconductor solid-state device of 4) is considered to be particularly promising to implement the large-scale quantum computation. As the quantum computation utilizing the semiconductor solid-state device, there are those using 4-1) a superconducting tunnel junction; 4-2) an impurity nuclear spin; and 4-3) an electronic state of a semiconductor quantum well structure.
As the quantum computation utilizing the electronic state of the semiconductor quantum well structure, Barenco proposal is made (A. Barenco, D. Deutsch, and A. Ekert, Phys. Rev. Lett., 74, 4083 (1995)). It will be described below.
First, the quantum well structure is a structure as shown in FIG. 3. It includes an alternate stack of semiconductor layers with a large energy gap such as AlGaAs and semiconductor layers with a small energy gap such as GaAs, and builds a well-type energy barrier for electrons and holes by sandwiching the semiconductor layers with the small energy gap by the semiconductor layers with the large energy gap, thereby confining the electrons and holes in the well. Since the structure is composed of different semiconductors, it is called a semiconductor hetero-structure, and the growth interface of the two semiconductors is called a hetero-interface.
In such a quantum well structure, since the electrons are confined only in its stack direction (Z direction), they have two degrees of freedom with losing the degree of freedom in the Z direction. Thus, the quantum well structure is called a two-dimensional semiconductor or quantum film structure (see, FIG. 4A). Confining the electrons in one more direction X or Y using the semiconductors with different energy gaps will result in a one-dimensional semiconductor or quantum wire structure with losing one more degree of freedom (see, FIG. 4B). Confining the electrons in the remaining two directions X and Y besides the Z direction using the semiconductors with different energy gaps will result in the zero-dimensional semiconductor or quantum dot or quantum box structure with losing the degree of freedom in all the directions X, Y and Z (see, FIG. 4C). The two-dimensional, one-dimensional and zero-dimensional semiconductor structures are called a low-dimensional quantum well structure in contrast with the three-dimensional bulk structure.
It is possible for the quantum dot structure to exclude higher order wave functions from all the wave functions (to cut off the higher order wave functions) by reducing the width (size) of each well confining the electrons to a very small size (on the order of a few nanometers) in all the three directions X, Y and Z. Thus, it can confine a single electron in each quantum dot. In addition, selecting the size of the dot makes it possible to fabricate the quantum dot structure with only the ground state and first excited state.
FIGS. 5A–5D are energy band diagrams illustrating the Barenco proposal. As illustrated in FIG. 5A, a structure is prepared which includes two adjacent quantum well structures a and b with different widths. In particular, to carry out the excitation control of a single electron, the quantum well is preferably a quantum dot that confines the electron in the three directions. As for the electronic states |a> and |b> confined in the quantum wells a and b, their ground states are denoted by |0>a and |0>b, and their first excited states by |1>a and |1>b. FIG. 5B illustrates is the energy levels in this case. Here, the indication |0>a|0>b represents that the electrons of both the wells a and b are in the ground state; |0>a|1>b represents that the electron of the well a is in the ground state and the electron of the well b is in the first excited state; |1>a|0>b represents that the electron of the well a is in the first excited state and the electron of the well b is in the ground state; and |1>a|1>b represents that the electrons of both the wells a and b are in the first excited state.
Irradiating the wells in this state with the electromagnetic wave with the energy corresponding to the energy difference Eb (=hωb/2π=hνb) between the two states |0>b and |1>b for a fixed time (time corresponding to a π pulse) can change the state |b> from |0>b to |1>b, or vice versa, thereby implementing the operation of the phase shifter. However, the operation of the controlled Not that changes the state |b> in response to the state |a> is unachievable.
In the Barenco proposal, the band structure of the quantum wells is inclined as illustrated in FIG. 5C by applying a voltage (Vext in FIG. 5C) across the barrier layers at the two ends of the quantum wells. In the quantum wells, the wave functions in the ground state and first excited state deviate in the opposite directions because of the quantum confined effect, and have opposite electric dipoles. In such a structure including quantum wells adjacent to each other, the energy of the |1>a|0>b and |0>a|1>b with the dipoles in the opposite directions becomes smaller than the energy of the |0>a|0>b and |1>a|1>b with the dipoles in the same direction because of the interaction between the electric dipoles. Owing to the interaction, the energy level diagram as illustrated in FIG. 5D is obtained, in which the energy difference Eb′ between the |1>a|0>b and |1>a|1>b is greater than the energy difference Eb″ between the |0>a|0>b and |0>a|1>b. Accordingly, pumping with the electromagnetic wave with the frequency ωb′ corresponding to Eb′ (=hωb′/2π=hνb′) makes it possible to selectively invert the |b> state only when the |a> is in the |1>a state.
However, trying to implement such logic gates using actual physical systems involves the following problems, and hence no example has been reported that experimentally demonstrates the Barenco proposal using actual physical systems up to now.
More specifically, the conventional Barenco proposal, which utilizes the optical transition between the quantum levels (inter-subband electrons) formed in the conduction band using the quantum well structures (see, FIG. 3), has the following problems because it uses the electronic state of the subband.
First, in the subband, the phonon scattering constitutes a decoherence factor. In general, the energy relaxation time from the first excited state to the ground state in the subband, which is very short on the order of picoseconds, presents a problem in the quantum operation.
Second, the transition wavelength (the wavelength of the inter-subband transition) from the first excited state to the ground state in the subband is determined by the depths of the quantum wells in the conduction band (energy discontinuous value ΔEc in the conduction band between the two semiconductors). The wavelength falls in about a far-infrared region (ultra-long wavelength of about 10 μm) when the semiconductors such as GaAs and InP are used. In this case, it is difficult to carry out the ultra-fast excitation control because of the lack of femtosecond laser technology operating at a speed of less than 100 femtoseconds.
Third, the maximum step number Ns of the quantum computation is estimated to be the quotient when the decoherence time (phase relaxation time) τ, at which the coherence term decays by a factor of e, is divided by the operation time Tg of the basic gate. Although it is considered that the number Ns must be greater than 1000–10000, since the times τ and Tg are each considered to have a limitation of a few picoseconds, the number Ns is becomes less than 10, making it very difficult to implement the large-scale quantum computation.